Auxiliary point on the semilocal convergence of Newton's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Ezquerro, J. A.¹  Hernandez-Veron, M. A.¹ 

[1] Univ La Rioja, Dept Math & Computat, Calle Madre Dios 53, Logrono 26006, La Rioja, Spain

关键词: Newton's method;    Semilocal convergence;    Majorizing sequence;    Error estimates;    Order of convergence;    Fred holm integral equation;   

DOI  :  10.1016/j.cam.2018.03.015

来源: Elsevier

【 摘 要 】

We use an auxiliary point on the semilocal convergence of Newton's method when the majorant principle of Kantorovich is applied to operators with high order derivatives satisfying a center Lipschitz type condition, so that we extend the classical conditions of these types, that are centered at the starting point of Newton's method, to other points belonging to the domain of definition of the operator involved. This extension provides a modification of the domain of starting points for Newton's method which allows increasing the choice of starting points. We illustrate this study with nonlinear Fredholm integral equations. (C) 2018 Elsevier B.V. All rights reserved.

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